Neutrino masses

I also noted at the same time that interactions between a pair of lepton doublets and a pair of scalar doublets can generate a neutrino mass, which is suppressed only by a factor M−1M^{-1}, and that therefore with a reasonable estimate of MM could produce observable neutrino oscillations. The subsequent confirmation of neutrino oscillations lends support to the view of the Standard Model as an effective field theory, with M somewhere in the neighborhood of 1016GeV10^{16} GeV. (Weinberg 09, p. 15)

Pauli with his argument and suggestion turned out to be right. The missing particle – called the neutrino by Enrico Fermi in 1933 – was finally directly detected in 1956, hence 26 years after its proposal. (Compare maybe to the Higgs boson for which detection came 50 years after prediction.)

But in view of this theorem, Bohr’s suggestion that energy conservation fails would have implied that fundamental physics is not governed by an action principle, something arguably more dramatic than some violation of some energy conservation might seem.

Today Pauli is widely acknowledged for holding up the conservation laws against Bohr’s proposal, see for instance (AP 06, p. 6), where it says:

Pauli’s belief in the absolute credibility of symmetry principles led him to defend conservation laws even when at that time the empirical evidence was doubtful. His prediction of the neutrino is a great example.

But on the other hand, it seems that Pauli’s respect for the conservation laws was not informed by Noether’s theorem, but rested rather on an intuitive feeling, for in (AP 06, p.5) Pauli is quoted as late as 1953 thus:

I am very much in favour of the general principle to bring empirical conservation laws and invariance properties in connection with mathematical groups of transformations of the laws of nature.

While this does support the correct answer, it seems to be a rather weak way of stating it, given that Noether’s theorem establishes this “connection” as a theorem, already back in 1915.

Similarly, in (AP 06, p. 6) Pauli is quoted as reacting to Bohr’s proposal by saying:

I am myself fairly convinced [...][...] that Bohr with his corresponding deliberations concerning a violation of energy conservation is entirely on the wrong track! [...][...] The idea of a violation of the conservation of energy in β-decay is and remains, in my opinion, cheap and very clumsy philosophy.

If Pauli had really been relying on symmetry and the Noether theorem, he could have said “provably wrong” instead of just “cheap and clumsy”. Especially since “clumsy” suggests “possible, even if not enjoyable”, where in fact it is impossible unless the whole foundations of physics are changed.